System and method for using microgyros to measure the orientation of a survey tool within a borehole

ABSTRACT

A system and method for determining an orientation of the survey tool within a borehole utilizes a survey tool including a plurality of rotation sensors each having a sensing axis and a direction of least acceleration sensitivity. The plurality of rotation sensors are mounted in a housing with their sensing axes generally parallel to one another and with their directions of least acceleration sensitivity generally non-parallel to one another. The survey tool further includes a controller adapted to calculate a weighted average of the detected angular rotation rates from the plurality of rotation sensors. The weighted average includes the detected angular rotation rate of each rotation sensor about its sensing axis weighted by the detected acceleration along its direction of least acceleration sensitivity.

CLAIM OF PRIORITY

This application is a continuation of U.S. patent application Ser. No.10/823,091, filed Apr. 13, 2004, which is incorporated in its entiretyby reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present application relates generally to systems and methods fordetermining the orientation of a survey tool within a borehole.

2. Description of the Related Art

Directional drilling for the exploration of oil and gas depositsadvantageously provides the capability of generating boreholes whichdeviate significantly relative to the vertical direction (that is,perpendicular to the Earth's surface) by various angles and extents. Incertain circumstances, directional drilling is used to provide aborehole which avoids faults or other subterranean structures (e.g.,salt dome structures). Directional drilling is also used to extend theyield of previously-drilled wells by reentering and milling through theside of the previously-drilled well, and drilling a new boreholedirected so as to follow the hydrocarbon-producing formation.Directional drilling can also be used to provide numerous boreholesbeginning from a common region, each with a shallow vertical portion, anangled portion extending away from the common region, and a terminationportion which can be vertical. This use of directional drilling isespecially useful for offshore drilling, where the boreholes are drilledfrom the common region of a centrally positioned drilling platform.

Rotatably steerable drilling systems which are configured to respond tocontrol signals by adjusting the direction of drilling are known in theprior art. Exemplary rotatably steerable drilling systems are disclosedby U.S. Pat. No. 6,659,201, U.S. Pat. No. 6,655,460, U.S. Pat. No.6,257,356, and U.S. Pat. No. 5,099,927, each of which is incorporated inits entirety by reference herein.

Directional drilling is also used in the context of horizontaldirectional drilling (“HDD”) in which a pathway is drilled for utilitylines for water, electricity, gas, telephone, and cable conduits.Exemplary HDD systems are described by Alft et al. in U.S. Pat. Nos.6,315,062 and 6,484,818. Such HDD systems typically drill alongrelatively short distances substantially horizontal to the surface anddo not drill very far below the surface. In addition, these HDD systemstypically drill holes which reemerge as well.

The pathway of a directionally drilled borehole is typically carefullyplanned prior to drilling, and the position and direction of thedrilling tool is repeatedly determined during the drilling process usingsurveys to map the pathway of the borehole relative to a fixed set ofknown coordinates. In certain types of wireline surveys, the drilling ofthe borehole is periodically halted and a survey tool is lowered intothe borehole. In some instances, the drilling assembly (i.e., the drillstring and the drilling tool, which includes the drill bit) is removedfrom the borehole so that the survey tool can be lowered into theborehole. In other types of wireline surveys, the drilling assemblyremains in the borehole and the survey tool is lowered into the drillingassembly. As the survey tool is guided along the borehole, it providesinformation regarding its orientation and location by sending signalsthrough a cable to the surface. This information is then used todetermine the pathway of the borehole. The survey tool is then removedfrom the borehole and drilling is continued, which may require returningthe drilling assembly to the borehole if it was removed for the survey.Such wireline surveys thus require extensive time and effort torepeatably stop drilling, insert the survey tool into the borehole, andremove the survey tool (and perhaps the drilling assembly) each time asurvey is performed. Since the costs associated with operation of adrilling system can be quite high, any time reductions in boreholesurveying can result in substantial cost savings.

In “measurement while drilling” (“MWD”) drilling systems, the surveytool is a component of the drilling system. In such drilling systems,the survey tool can be a component of the drilling tool, typically inproximity to the drill bit, and it remains within the boreholethroughout the drilling process. MWD survey measurements of theorientation and location of the MWD survey tool can be made withoutremoving the drilling assembly from the borehole. Typically, MWD surveymeasurements are taken during periods in which additional drill pipesare connected to extend the drill string and the drilling assembly issubstantially stationary, which takes approximately one to two minutesto a few minutes. Use of MWD surveys saves time during operation of thedrilling system by eliminating the need to stop the drilling process orto remove and replace the survey tool (and perhaps the drillingassembly) in order to survey the pathway of the borehole. Such MWDdrilling systems are known in the art.

In “logging while drilling” (“LWD”) drilling systems, the drillingsystem includes a survey tool and a logging string having one or moregeophysical sensors configured to provide information regarding thegeological formations surrounding the borehole at various depths.Examples of geophysical sensors compatible with LWD drilling systemsinclude, but are not limited to, geophones configured to make porosityand/or density measurements using sonar, gamma-ray detectors configuredto detect gamma rays from the surrounding geological formations, andresistivity sensors configured to make porosity and/or pore contentmeasurements. In addition, certain LWD logging strings include calipersconfigured to mechanically sense aspects of the borehole and its casing(e.g., size, amount of wear). In certain instances, the survey tool is acomponent of the logging string, while in other instances, the surveytool is in proximity to the logging string. Such LWD drilling systemsare known in the art.

Gyroscopes, together with accelerometers, have been used in survey toolsto measure the azimuth and the inclination of a borehole at a givendepth, and the high-side toolface and/or the azimuthal toolface of thesurvey tool at the same depth. Such measurements typically utilize aminimum number of sensitive gyroscope axes (i.e., the gyroscope providesangular rotation rate information for rotations about these axes).Existing survey tools include only the minimum number of sensitivegyroscope axes to perform the desired measurements, due to the highcosts of spinning-wheel and ring-laser gyroscopes.

SUMMARY OF THE INVENTION

In certain embodiments, a survey tool determines an orientation of thesurvey tool within a borehole. The survey tool comprises a plurality ofrotation sensors. Each rotation sensor has a sensing axis and adirection of least acceleration sensitivity. Each rotation sensor isadapted to generate a first signal indicative of a detected angularrotation rate about its sensing axis. The plurality of rotation sensorsare mounted in a housing with their sensing axes generally parallel toone another and with their directions of least acceleration sensitivitygenerally non-parallel to one another. The survey tool further comprisesa plurality of acceleration sensors mounted in the housing. Eachacceleration sensor has a sensing direction. Each acceleration sensor isadapted to generate a second signal indicative of detected accelerationalong its sensing direction. The survey tool further comprises acontroller adapted to receive a first signal from each of the pluralityof rotation sensors and a second signal from each of the plurality ofacceleration sensors. The controller is adapted to calculate a weightedaverage of the detected angular rotation rates from the plurality ofrotation sensors. The weighted average includes the detected angularrotation rate of each rotation sensor about its sensing axis weighted bythe detected acceleration along its direction of least accelerationsensitivity.

In certain embodiments, a control system of a rotatably steerabledrilling system is configured to drill in a selected drilling directionof a plurality of drilling directions. The control system is configuredto adjust the selected drilling direction. The control system comprisesa plurality of rotation sensors. Each rotation sensor has a sensing axisand a direction of least acceleration sensitivity. Each rotation sensoris adapted to generate a first signal indicative of a detected angularrotation rate about its sensing axis. The plurality of rotation sensorsare mounted in a housing with their sensing axes generally parallel toone another and with their directions of least acceleration sensitivitygenerally non-parallel to one another. The control system furthercomprises a plurality of acceleration sensors mounted in the housing.Each acceleration sensor has a sensing direction. Each accelerationsensor is adapted to generate a second signal indicative of detectedacceleration along its sensing direction. The control system furthercomprises a controller adapted to receive a first signal from each ofthe plurality of rotation sensors and a second signal from each of theplurality of acceleration sensors. The controller is adapted tocalculate a weighted average of the detected angular rotation rates fromthe plurality of rotation sensors. The weighted average includes thedetected angular rotation rate of each rotation sensor about its sensingaxis weighted by the detected acceleration along its direction of leastacceleration sensitivity.

In certain embodiments, a method determines an orientation of a surveytool within a borehole. The method comprises providing a plurality ofrotation sensors. Each rotation sensor has a sensing axis and adirection of least acceleration sensitivity. The plurality of rotationsensors have their sensing axes generally parallel to one another andtheir directions of least acceleration sensitivity generallynon-parallel to one another. The method further comprises obtaining adetected angular rotation rate from each rotation sensor. Each detectedangular rotation rate being about the sensing axis of the correspondingrotation sensor. The method further comprises obtaining a detectedacceleration along the directions of least acceleration sensitivity ofeach of the rotation sensors. The method further comprises calculating aweighted average of the detected angular rotation rates from theplurality of rotation sensors. The weighted average includes thedetected angular rotation rate of each rotation sensor about its sensingaxis weighted by the detected acceleration along its direction of leastacceleration sensitivity.

In certain embodiments, a rotatably steerable drilling system isprovided. The drilling system comprises a drill string configured todrill in a selected direction of a plurality of directions. The drillstring comprises a drill bit. The drilling system further comprises asurvey tool in proximity to the drill bit. The survey tool comprises aplurality of rotation sensors. Each rotation sensor has a sensing axisand a direction of least acceleration sensitivity. Each rotation sensoris configured to generate a first signal indicative of a detectedangular rotation rate about its sensing axis. The plurality of rotationsensors is mounted in a housing with their sensing axes generallyparallel to one another and with their directions of least accelerationsensitivity generally non-parallel to one another. The survey toolfurther comprises a plurality of acceleration sensors mounted in thehousing. Each acceleration sensor has a sensing direction. Eachacceleration sensor is configured to generate a second signal indicativeof detected acceleration along its sensing direction. The survey toolfurther comprises a controller configured to receive a first signal fromeach of the plurality of rotation sensors and a second signal from eachof the plurality of acceleration sensors. The controller is configuredto calculate a weighted average of the detected angular rotation ratesfrom the plurality of rotation sensors. The weighted average includesthe detected angular rotation rate of each rotation sensor about itssensing axis weighted by the detected acceleration along its directionof least acceleration sensitivity. The controller is further configuredto generate a third signal indicative of the weighted average. Thedrilling system further comprises a steering mechanism configured toadjust the selected direction in response to the third signal from thecontroller.

For purposes of summarizing the invention, certain aspects, advantagesand novel features of the invention have been described herein above. Itis to be understood, however, that not necessarily all such advantagesmay be achieved in accordance with any particular embodiment of theinvention. Thus, the invention may be embodied or carried out in amanner that achieves or optimizes one advantage or group of advantagesas taught herein without necessarily achieving other advantages as maybe taught or suggested herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates a survey tool in accordance withembodiments described herein.

FIG. 2A schematically illustrates a vibrating-wheel microgyro which issensitive to angular rotation rates about a sensing axis in themicrogyro's ground plane.

FIG. 2B schematically illustrates a resonating-mass microgyro which issensitive to angular rates about a sensing axis generally perpendicularto the microgyro's ground plane.

FIGS. 3A and 3B schematically illustrate a plurality of rotation sensorscomprising three resonant-mass microgyros in accordance with embodimentsdescribed herein.

FIGS. 4A and 4B schematically illustrate alternative embodiments of apacked unit of microgyros with sensing axes parallel to the sensing axesof the microgyros of another packed unit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Making gyroscopic measurements of the orientation and position of awireline geophysical instrument package using a survey tool or of adrilling tool while drilling using a measurement-while-drilling (MWD)survey tool is a challenging task due in part to the extreme conditionsto which the survey tool is exposed. For example, the survey tool isoften exposed to accelerations which can influence or disruptmeasurements of the angular rotation rate about a sensing axis. Sincesome gyroscope errors are a function of sensed acceleration, smallaccelerations (e.g., fractions of the gravitational acceleration of 9.8meters/sec²) can cause significant angular rate errors. Vibrations cancreate oscillations in the output from the gyroscope, leading to anunfavorable random error increase. In addition, for gyroscopes usingfeedback loops, such high frequency vibrations can lead to undesirableerrors.

FIG. 1 schematically illustrates a survey tool 10 in accordance withembodiments described herein. The survey tool 10 can be used fordetermining an orientation of the survey tool as part of a wirelinegeophysical instrument package or of a drilling tool of a drillingsystem adapted to drill a borehole into the Earth's surface. The surveytool 10 comprises a plurality of rotation sensors 30. Each rotationsensor 30 has a sensing axis 32 and a direction of least accelerationsensitivity 34. Each rotation sensor 30 is adapted to generate a firstsignal 36 indicative of a detected angular rotation rate about itssensing axis 32. The plurality of rotation sensors 30 are desirablymounted in a housing 38 with their sensing axes 32 generally parallel toone another and with their directions of least acceleration sensitivity34 generally non-parallel to one another. The survey tool 10 furtherdesirably comprises a plurality of acceleration sensors 40 mounted inthe housing 38. Each acceleration sensor 40 has a sensing direction 42and is adapted to generate a second signal 46 indicative of detectedacceleration along its sensing direction 42. The survey tool 10 furthercomprises a controller 50 adapted to receive the first signals 36 fromthe plurality of rotations sensors 30 and the second signals 46 from theplurality of acceleration sensors 40. The controller 50 is adapted tocalculate a weighted average of the detected angular rotation rates fromthe plurality of rotation sensors 30. The weighted average includes thedetected angular rotation rate of each rotation sensor 30 about itssensing axis 32 weighted by the detected acceleration along itsdirection of least acceleration sensitivity 34.

In certain embodiments, the plurality of rotation sensors 30 comprises aplurality of gyroscopes. The gyroscopes utilize the Coriolis effect inwhich a mass M moving with a velocity v in a reference frame rotating atan angular velocity Ω sees a Coriolis force F_(Coriolis)=2Mv×Ω. Incertain such embodiments, the gyroscopes are “microgyros,” which aregyroscopes micromachined on a chip using photolithography and othertechniques developed originally for semiconductor fabrication. Exemplarymicrogyros include, but are not limited to, the PLCC44 vibrating-wheelmicrogyro available from Robert Bosch GmbH of Stuttgart, Germany, andthe ADXRS150 resonating-mass microgyro available from Analog Devices,Inc. of Norwood, Mass. Each of these two microgyros is manufactured as amicrochip in a generally square package with a thickness smaller thanthe lengths of its sides. Certain embodiments of the sensor system 10can use microgyros of a single type, or can utilize a mixture of types.In the embodiments described below, the Analog Devices-type microgyrosare used to describe various features. Persons skilled in the art canrecognize that other types of microgyros (or gyroscopes in general) arecompatible, alone or in combination with other types, with embodimentsdescribed herein.

FIG. 2A schematically illustrates the vibrating-wheel microgyro 60 whichis sensitive to angular rotation rates about a sensing axis 32 in themicrogyro's ground plane. The microgyro 60 of FIG. 2A includes a wheel62 with an axis of symmetry 64, about which the wheel 62 is driven tovibrate. Upon rotation about the sensing axis 32 (which is in the planeof the wheel 62), the wheel 62 tilts, and this tilting is measured bydetecting the differential capacitance between the wheel 62 and theelectrodes 66 under the wheel 62. Such microgyros 60 can also includeelectronic circuitry to convert the differential capacitancemeasurements into a first signal indicative of the angular rotation rateabout the sensing axis 32. In certain embodiments, such microgyros 60can be used to detect two in-plane rotational axes with a singlevibrating wheel 62. Further description of such vibrating-wheelmicrogyros 60 is provided by Darrell Teegarden et al. in “How to Modeland Simulate Microgyroscope Systems,” IEEE Spectrum, July 1998, Volume35, Number 7, pp. 66-75, which is incorporated in its entirety byreference herein.

FIG. 2B schematically illustrates the resonating-mass microgyro 70 whichis sensitive to angular rates about a sensing axis 32 generallyperpendicular to the microgyro's ground plane. The microgyro 70 of FIG.2B includes a resonating mass 72 coupled by springs 74 to an inner frame76. The inner frame 76 is coupled to an outer frame 78 by springs 80.Sense fingers 82 on the inner frame 76 and the outer frame 78 are usedto capacitively detect displacement of the inner frame 76 relative tothe outer frame 78. Such microgyros 70 can also include electroniccircuitry to convert the capacitance measurements into a first signalindicative of the angular rotation rate about the sensing axis 32.Further descriptions of such resonant-mass microgyros 70 are provided byGeen et al. in U.S. Pat. Nos. 5,635,638, 5,635,640, and 6,122,961, aswell as by J. Geen et al. in “New iMEMS® Angular-Rate-SensingGyroscope,” Analog Dialogue, 2003, Volume 37, Number 3, pp. 1-4, each ofwhich are incorporated in its entirety by reference herein.

In general, microgyros are sensitive to accelerations or vibrationswhich can cause movements which can be erroneously attributed to beingdue to Coriolis forces, thereby causing measurement errors. For example,accelerations or vibrations of the resonating-mass microgyro 70 alongthe direction of relative movement between the inner frame 76 and theouter frame 78 can cause displacements which are erroneously interpretedto be due to changes of the angular rotation rate about the sensing axis32. Conversely, the resonating-mass microgyro 70 is less sensitive toaccelerations or vibrations along the direction perpendicular to thedirection of relative movement between the inner frame 76 and the outerframe 78 (i.e., along the resonant displacement direction of the mass72). For resonating-mass microgyros 70, the resonant displacementdirection of the mass 72 is the direction of least accelerationsensitivity. Other types of microgyros, including vibrating-wheelmicrogyros 60, also have directions of least acceleration sensitivitydictated by the geometry of the microgyro. Microgyros experiencingaccelerations or vibrations not due to the Coriolis force thus providetheir most reliable measurements when these accelerations or vibrationsare along the direction of least acceleration sensitivity.

FIGS. 3A and 3B schematically illustrate a plurality of rotation sensors30 comprising three resonant-mass microgyros 70 in accordance withembodiments described herein. Other embodiments can utilize a pluralityof rotation sensors 30 comprising two, four, five, six, or any othernumber of rotation sensors 30. In certain embodiments, the microgyros 70of FIGS. 3A and 3B, have packaging which is small enough for use in thetight confines of a borehole (e.g., the Analog Device Part No. ADXRS150has packaging with dimensions of approximately 7 millimeters by 7millimeters by 3 millimeters). The smallest inside diameter of a drillpipe is typically less than or equal to approximately two inches.

To maintain their relative positions and orientations to a high degreeof accuracy, the rotation sensors 30 can be secured from moving relativeto one another under temperature variations, heavy vibrations, and otherenvironmental conditions experienced by the rotation sensors 30. Incertain embodiments, as schematically illustrated by FIG. 3A, eachmicrogyro 70 is mounted in a gyro housing 80 and epoxy 82 can be used tocouple the gyro housings 80 together into one packed unit 90 ofgenerally cubical form with the sensing axes 32 of the microgyros 70oriented colinearly. The packed unit 90 can then be described as havinga sensing axis 92 aligned with the sensing axes 32 of the microgyros 70.The cubical form is especially suitable for being mounted in the housing38 along any of the three principle axes of the survey tool 10, or anyother axes that may be of interest. In certain embodiments in which thedrilling system comprises a MWD tool, the housing 38 of the survey tool10 is in proximity to the drill bit or the drilling tool (which includesthe drill bit), while in other MWD embodiments, the housing 38 of thesurvey tool 10 is a component of the drilling tool. In wirelineembodiments, the housing 38 of the survey tool 10 is insertable into theborehole after the drill string has been removed or is insertable intothe drill string itself. Other embodiments utilize other configurationsfor mounting the rotation sensors 30.

FIG. 3B provides a top view of each of the three microgyros 70 of thepacked unit 90 of FIG. 3A to schematically illustrate the orientationsof these microgyros 70. The microgyros 70 are rotated relative to oneanother such that their directions of least acceleration sensitivity 34are non-parallel to one another. In certain embodiments, the directionsof least acceleration sensitivity 34 of the rotation sensors 30 arespread substantially equally over approximately 180 degrees. Since anexternal vibration can have any direction relative to the packed unit90, the directions of least acceleration sensitivity 34 of the differentmicrogyros 70 of the packed unit 90 are spread evenly to maximize thelikelihood for having at least one microgyro 70 with acceptably lowacceleration sensitivity. For example, for the three resonant-massmicrogyros 70 of FIG. 3B, the directions of least accelerationsensitivity 34 are at approximately 0 degrees, approximately 60 degrees,and approximately 120 degrees. In such an embodiment, the direction ofany acceleration within the microgyro's ground plane is not more thanapproximately 30 degrees away from one of the directions of leastacceleration sensitivity 34.

Advantageously, use of a packed unit 90 with three microgyros 70 canprovide the combination of small size and sufficient data measurementsto facilitate high accuracy measurements. Where greater accuracy isdesired, a packed unit with four microgyros can provide such greateraccuracy with limited additional size. Using more rotation sensors 30can improve the resultant accuracy of the calculated weighted average ofthe readings from the rotation sensors 30.

Other embodiments can use other relative angles (e.g., using fourrotation sensors 30 with directions of least acceleration sensitivity 34at approximately 0, 45, 90, and 135 degrees). While it is statisticallypreferable to have the directions of least acceleration sensitivity 34spread equally over a range of degrees, in other embodiments, thedirections of least acceleration sensitivity 34 are not spread equallyover a range of degrees.

In certain embodiments, multiple packed units 90 may be used withparallel sensing axes 92. FIG. 4A schematically illustrates a pair ofpacked units 90 with sensing axes 92 of both packed units 90 paralleland colinear with one another. FIG. 4B schematically illustrates a pairof packed units 90 with the sensing axis 92 of one packed unit 90parallel to the sensing axis 92 of the other packed unit 90.

In certain embodiments, multiple packed units 90 having parallel sensingaxes 92 are mounted in the housing 38 but spaced apart from one another.In such embodiments, the packed units 90 can experience differentvibration patterns so that when one packed unit 90 undergoesacceleration or vibration, the other packed unit 90 may provide usablemeasurements. However, such embodiments can also experience bendingbetween the packed units 90 such that the packed units 90 becomemisaligned relative to one another.

In certain embodiments, each packed unit 90 can have the directions ofleast acceleration sensitivity 34 of its microgyros 70 spreadsubstantially equally over approximately 180 degrees (i.e., each packedunit 90 covers approximately 180 degrees). In certain other embodiments,each packed unit 90 can have the directions of least accelerationsensitivity 34 of its microgyros 70 spread over less than 180 degrees,but the directions of least acceleration sensitivity 34 of all themicrogyros 70 are spread substantially equally over approximately 180degrees (i.e., the sum of the packed units 90 covers approximately 180degrees).

In certain embodiments, the plurality of acceleration sensors 40comprises accelerometers each of which provides a signal indicative ofdetected acceleration along its sensing direction 42. The accelerationsensors 40 can be conventional accelerometers commonly used in surveytools, or can be micromachined accelerometers. Exemplary accelerometersinclude, but are not limited to, those described by N. Yazdi et al. in“Micromachined Inertial Sensors,” Proc. of the IEEE, August 1998, Vol.86, No.8, pp. 1640-1659, which is incorporated in its entirety byreference herein.

In certain embodiments, the plurality of acceleration sensors 40includes enough accelerometers to measure the two-dimensionalacceleration in the plane defined by the directions of leastacceleration sensitivity 34 of the rotation sensors 30. In suchembodiments, the acceleration in this plane detected by the plurality ofacceleration sensors 40 is decomposed into its components along thedirections of least acceleration sensitivity 34 of the rotation sensors30. In certain embodiments, the plurality of acceleration sensors 40 aremounted in the housing 38 with their sensing directions 42 generallyparallel to the directions of least acceleration sensitivity 34 of theplurality of rotation sensors 30. In such embodiments, the accelerationsdetected by the acceleration sensors 40 correspond to the components ofthe detected acceleration along the directions of least accelerationsensitivity 34 of the plurality of rotation sensors 30. In otherembodiments, the plurality of acceleration sensors 40 are mounted in thehousing 38 such that vector analysis can be used to determine thecomponents of the detected acceleration along the directions of leastacceleration sensitivity 34 of the plurality of rotation sensors 30.Other embodiments utilize other configurations for mounting theacceleration sensors 40.

In certain embodiments, the controller 50 comprises a microprocessoradapted to receive the first signals 36 from the plurality of rotationssensors 30 and the second signals 46 from the plurality of accelerationsensors 40. The controller 50 of certain embodiments comprisessufficient memory to facilitate the calculations. In certainembodiments, the controller 50 is wholly or partly mounted in thehousing 38. In other embodiments, the controller 50 is positioned awayfrom the housing 38, but is coupled to the rotation sensors 30 and theacceleration sensors 40 mounted in the housing 38.

In certain embodiments, the survey tool 10 is part of a rotatablysteerable drilling system which is configured to adjust the direction ofdrilling in response to signals from the controller 50 of the surveytool 10. In certain such embodiments, the rotatably steerable drillingsystem comprises a control system which is coupled to a steeringmechanism for the rotatably steerable drill string. In certainembodiments, the control system comprises the controller 50, while inother embodiments, the control system receives signals from controller50. The control system sends control signals to the steering mechanismin response to the data from the survey tool 10.

The controller 50 is adapted to calculate a weighted average of thedetected angular rotation rates from the plurality of rotation sensors30. The weighted average includes the detected angular rotation rate ofeach rotation sensor 30 about its sensing axis 32 weighted by thedetected acceleration along its direction of least accelerationsensitivity 34. The resultant weighted average angular rotation rateR_(p) can be expressed by the following equations: $\begin{matrix}{{R_{p} = \frac{\sum\limits_{i}^{\quad}\left( {R_{i}*W_{i}} \right)}{\sum\limits_{i}^{\quad}W_{i}}},\quad{and}} & (1) \\{W_{i} = \left( {A_{i}/A_{g}} \right)^{2}} & (2)\end{matrix}$where R_(i) is the measured angular rotation rate from rotation sensori, A_(g) is the ground plane acceleration, and A_(i) is the component ofthe ground plane acceleration along the direction of least accelerationsensitivity of rotation sensor i.

In certain embodiments, the first signals 36 are provided continually bythe rotation sensors 30 to the controller 50 and the second signals 46are provided continually by the acceleration sensors 40 to thecontroller 50. In certain such embodiments, the controller 50 accessesthe first signals 36 and the second signals 46 at a discrete frequency.Due to possible high frequency vibrations, the discrete frequency of thecontroller 50 is preferably chosen to be high. While the chosen discretefrequency will be limited by the electronics, it is preferably in thekilohertz range. For example, the controller 50 can access the firstsignals 36 from each of the three rotation sensors 30 of a packed unit90 and can access the second signals 46 from each of the threeacceleration sensors 40 corresponding to these rotation sensors 30. Thetime period over which the rate measurement is made (i.e., the timeelapsed from accessing the first measurement to accessing the lastmeasurement used for calculating a weighted average angular rotationrate) is defined as an “epoch.” The controller 50 then calculates aweighted average angular rotation rate for each epoch. In certainembodiments, it is desirable to have epochs as short as possible so asto provide frequent evaluations of the weighted average angular rotationrate.

In certain embodiments utilizing three or more rotation sensors 30, thestandard deviation can be used to provide real-time quality control ofthe measured angular rotation rate. The term “real-time quality control”is used broadly herein to mean selective exclusion from the calculationof apparently-erroneous measurements from one or more rotation sensors30 as the measurements are being made. The standard deviation SD_(p) forthe weighted average angular rotation rate R_(p) can be estimated by thefollowing equation: $\begin{matrix}{{SD}_{p} = {\sqrt{\frac{\sum\limits_{i}^{\quad}{W_{i}*\left( {R_{i} - R_{p}} \right)^{2}}}{\left( {N - 1} \right)*{\sum\limits_{i}^{\quad}W_{i}}}}.}} & (3)\end{matrix}$where N is the number of rotation sensors 30 included in the weightedaverage angular rotation rate. In certain embodiments, quality controlcalculations are performed within substantially simultaneously with thecorresponding measurements, while in other embodiments, the calculationsare performed at regular intervals (for example, every second, every fewseconds, or every ten seconds).

In certain embodiments, a rotation sensor 30 not satisfying apredetermined condition is excluded from the weighted average angularrotation rate R_(p). Such rotation sensors 30 may be malfunctioning,e.g., due to experiencing excessive acceleration, temperatures, etc. Incertain such embodiments, the predetermined condition is provided by thefollowing equation:|R _(i) −R _(p) |<T*SD _(P)  (4)where T is a tolerance factor, which in certain embodiments equals 3,and in other embodiments equals 5.

The tolerance factor of certain embodiments is taken from the normaldistribution. For example, 50% of the measurements will be within ±0.67σof the mean of the distribution, 95% of the measurements will be within±1.96σ of the mean of the distribution, and 99.9% of the measurementswill be within ±3.29σ of the mean of the distribution. The tolerancefactor in such embodiments is chosen depending on the desired tolerancefor getting a result offset by accepting a bad measurement, or forthrowing away a good measurement. A low tolerance number corresponds toavoiding using bad measurements and a high tolerance number correspondsto avoiding excluding good measurements.

If one or more rotation sensors 30 are excluded, a new weighted averageangular rotation rate R_(p) can be calculated using only the remainingrotation sensors 30. If there are three or more remaining rotationsensors 30, a new standard deviation SD_(p) can be calculated using onlythe remaining rotation sensors 30. In certain embodiments, the readingsfrom the remaining rotation sensors 30 can then be tested using the newstandard deviation in Equation 4.

In certain other embodiments, the rotation sensor 30 furthest from theweighted average angular rotation rate R_(p) is excluded, and theweighted average is recalculated. In alternative embodiments, the secondsignals 46 from the acceleration sensors 40 can be used to determinewhich rotation sensors 30 to exclude from the weighted average angularrotation rate R_(p). For example, if an acceleration larger than apredetermined magnitude is detected along a direction of particularsensitivity of one of the rotation sensors 30 (e.g., perpendicular tothe direction of least acceleration sensitivity 34), that rotationsensor 30 can be excluded from the calculation of the weighted averageangular rotation rate R_(p). In certain embodiments, the magnitude ofacceleration that would be enough to exclude a rotation sensor 30 fromthe calculation is set after testing the survey tool 10.

In still other embodiments, other parameters can be used to select whichrotation sensors 30 to exclude from the weighted average angularrotation rate R_(p). For example, in embodiments in which each rotationsensor 30 has a corresponding temperature sensor, the rotation sensor 30can be excluded if its temperature is above a predeterminedmaximum-value. Similarly, the rotation sensor 30 can be excluded if itstemperature is below a predetermined minimum value. In either case, theweighted average is recalculated by excluding the detected angularrotation rates obtained from the rotation sensors with temperaturesabove the predetermined maximum value or below the predetermined minimumvalue.

In embodiments in which two or more packed units 90 are used with theirsensing axes 92 parallel to a principle axis, a weighted average angularrotation rate R_(a) can be calculated for the principle axis based onthe weighted average angular rotation rates R_(p) of the packed units 90using the following equation: $\begin{matrix}{{R_{a} = \frac{\sum\limits_{j}^{\quad}\left( {R_{p,j}*W_{j}} \right)}{\sum\limits_{j}^{\quad}W_{j}}},\quad{and}} & (5) \\{W_{j} = \left( \frac{{SD}_{p,j}*N_{e,j}}{N} \right)^{2}} & (6)\end{matrix}$where R_(pj) is the weighted average angular rotation rate of packedunit j, SD_(pj) is the standard deviation of packed unit j, N is thetotal number of rotation sensors in each packed unit, and N_(ej) is thenumber of rotation sensors 30 that are used in each packed unit j.Real-time quality control of the measured angular rotation rate can beprovided by excluding packed units 90 using criteria similar to thosedescribed above in relation to excluding rotation sensors 30.

In certain embodiments, predictive filtering (e.g., Kalman-filteringcalculations) can be used to calculate the averaged angular rotationrate. Kalman filtering is a predictive filtering technique developed forstatistical adjustments of navigational measurements with atime-dependent position vector. In such Kalman filtering, the expectedposition and speed at a given moment can be calculated using a measuredposition and velocity at an earlier moment. Upon measuring the positionand velocity at the given moment, the measured and expected values canbe used to continue calculating later-expected values of the positionand velocity and monitoring the behavior of the system.

A similar predictive filtering technique can also be applied to the datagenerated by a plurality of rotation sensors 30. Instead of thetime-dependent position vector and utilizing the full navigationalmeasurements of traditional Kalman filtering, embodiments describedherein utilizing Kalman filtering have a time-dependent angular rotationrate and utilize angular rotation sensor measurements and accelerometermeasurements. Additional information regarding Kalman filtering isprovided by U.S. Pat. No. 4,537,067 to Sharp et al., U.S. Pat. No.4,987,684 to Andreas et al., U.S. Pat. No. 6,381,858 B1 to Shirasaka,and U.S. Pat. No. 6,453,239 B1 to Shirasaka et al., each of which isincorporated in its entirety by reference herein.

In certain embodiments, a multistate Kalman filter can be used. Thestates used can vary in different implementations of the filtering. Forexample, in certain embodiments, it is desirable to control the biasdrift of the microgyros due to accuracy demands, etc. The bias drift istypically the greatest source of error in a gyroscopic measurement. Thebias varies with time, and can not be totally compensated for bypredetermined calibration correction terms. Bias correction based on areal-time bias estimate can be significantly better and result in a moreaccurate angular rate measurement. The states (i.e., unknowns) of themultistate Kalman filter can include, but are not limited to, theangular rotation rate about the sensing axis, the rate of change of theangular rotation rate, the bias of each used microgyro, the rate ofchange of these biases, and small corrections to calibration terms(e.g., scale factor). In embodiments in which three or more packed units90 or three or more multiple packed unit axes are used, in addition tothe states listed above, the multistate Kalman filter can also treat theazimuth, inclination, high-side toolface, and azimuthal toolface asunknowns to be calculated. Such embodiments can also be self-monitoringand capable of avoiding divergence of the calculation by resetting orstopping the calculation upon detection of predetermined conditions, asdescribed below.

In certain embodiments, measurements of a given epoch are run throughthe real-time quality control method described above to detectmeasurements to be excluded from the calculation. The remainingmeasurements can then be inputted into the Kalman filter. In certainembodiments, the Kalman filter includes the following matrices:

-   -   X_(k)=vector matrix of the states of the filter at epoch k;    -   Σ_(s,k)=covariance matrix of the states at epoch k;    -   A_(k)=matrix linking the states and the measurements;    -   W_(k)=vector matrix with the measurement rate offsets at epoch        k;    -   Σ_(m,k)=covariance matrix of the measurements at epoch k;    -   Φ_(k)=matrix describing the transition from epoch (k−1) to epoch        k; and    -   Σ_(Φ,k)=covariance matrix of the transition from epoch (k−1) to        epoch k.        In such embodiments, the Kalman filtering procedure can use the        following equations:        X _(k′)=Φ_(k) *X _(k−1);  (7)        Σ_(s,k′)=Φ_(k)*Σ_(s,k−1)*Φ_(k) ^(T)*Σ_(Φ,k);  (8)        X _(k) =X _(k′)−Σ_(s,k′) *A _(k) ^(T)*(Σ_(m,k) +A _(k)*Σ_(s,k′)        *A _(k) ^(T))⁻¹* (A _(k) *X _(k′) +W _(k)); and  (9)        Σ_(s,k)=Σ_(s,k′)−└Σ_(s,k′) *A _(k) ^(T)*(Σ_(m,k) +A        _(k)*Σ_(s,k′) *A _(k) ^(T))⁻¹ ┘*A _(k)*Σ_(s,k′).  (10)

In certain embodiments, the controller 50 is adapted to monitor theKalman filter calculation to provide advantageous capabilities. Certainsuch embodiments allow the controller 50 to avoid divergence of theKalman filter calculation. Upon occurrence of a predetermined condition,the controller 50 can stop the Kalman filter calculation or reset thecalculation to a new state and restart. Examples of predeterminedconditions include, but are not limited to, any of the states exceedinga preset maximum level, any of the states below a preset minimum level,and the standard deviation of any of the states exceeding a presetmaximum level. In other embodiments, the covariance matrices can providehelpful information to determine whether the Kalman filter calculationbegins to diverge.

In other embodiments, the controller 50 is adapted to provide activegross error control by monitoring the rotation sensors 30 over time. Thecontroller 50 can then exclude those rotation sensors 30 which areapparently having difficulties providing accurate measurements.Similarly, in other embodiments, the controller 50 is adapted to monitorthe acceleration sensors 40 over time. Such embodiments advantageouslyincrease the time between fatal failures of the survey tool 10, whichcan be particularly important in oil and gas exploration where delayscan be costly.

In other embodiments, the controller 50 is adapted to provide real-timetuning of the rotation sensors 30. The term “real-time tuning” is usedbroadly herein to mean adjusting the gain of the rotation sensors 30while measurements are being made. Existing gyroscopes have limitedranges of high accuracy angular rotation rate measurements. Due to thelarge rate difference between the Earth's rotation (a few degrees perhour) and the fast rotation of the drilling tool 20 (hundreds of degreesper second), existing gyroscopes are unable to provide high accuracyangular rotation rate measurements across the whole range ofmeasurements. By monitoring the Kalman filter calculation, thecontroller 50 can characterize the present signal bandwidth andcalculate an expected noise level. This noise level can be used by thecontroller 50 to adjust the gain of the rotation sensors 30, therebyimproving the accuracy.

Embodiments described herein which use packed units 90 of microgyros canbe made more economically than existing survey tools which usespinning-wheel or ring-laser gyroscopes. Such embodiments can utilizemore than the minimum number of sensitive gyroscope axes (e.g., morethan one gyroscope per sensitive gyroscope axis), thereby increasing theaccuracy of the resultant measurements. In certain embodiments, thedirections of least acceleration sensitivity 34 of the rotation sensors30 of each packed unit 90 are substantially equally spread out. In suchembodiments in which the packed unit 90 comprises four or moremicrogyros, the controller 50 can utilize the Kalman filter calculationto detect whether one of the microgyros is providing erroneousmeasurements, remove the erroneous microgyro measurement from thecalculation, and provide an angular rotation rate measurement utilizingthe remaining microgyros with sufficient reliability.

Certain embodiments can provide real-time calibration based on themultiple-state Kalman filtering. For two or more packed units 90 havingtheir sensing axes 32 substantially parallel to one another, anymisalignments between the packed units 90 (e.g., due to non-systematicmovements) can result in their sensing axes 32 not being parallel. Asthe measurements continue, the controller 50 can track thesemisalignments and calibrate them mathematically in real-time to reduceor eliminate their contribution to the average angular rotation rate. Incertain embodiments, the misalignment will be one of the unknown statesof the Kalman filter. In addition, any biases of the microgyros can becalibrated over time by the controller 50 and incorporated appropriatelyinto the measurements of the angular rotation rate. In certainembodiments, the bias will be one of the unknown states of the Kalmanfilter. In such embodiments, the initial measurements may haverelatively high uncertainty, but as the measurements continue, theuncertainty can be reduced using information from the covariancematrices.

Example of Kalman Filter Implementation

To illustrate the implementation of the Kalman filter calculation, anexemplary embodiment has two microgyros packed together with theirsensing axes 32 colinear with one another. In this exemplary embodiment,the following assumptions have been made:

-   -   1. The first microgyro (MG_(a)) is perfectly mounted, and        measures the full tool axis (z-axis) angular rotation rate.    -   2. The second microgyro (MG_(b)) is inaccurately mounted to be        misaligned with an angle M with respect to the tool axis.    -   3. Each microgyro has an unknown time-dependent bias error        (B_(a)(t) and B_(b)(t), respectively) for which it is desirable        to correct.    -   4. The frequency of sampling the measurements from the        microgyros is high enough to neglect angular accelerations        between subsequent samplings.    -   5. The combined unit is exposed to a tool axis angular rate        ω_(z), which is a function of time.    -   6. The tool axis angular rate ω_(z)(t) is the principal unknown        quantity, and the desired measured quantity.    -   7. The two microgyro biases, B_(a) and B_(b), and M are the        secondary unknown quantities.    -   8. The unknown quantities can be expressed as a vector:        X(t)=[ω_(z)(t) B _(a)(t) B _(b)(t) M] ^(T).

All four of the parameters ω_(z), B_(a), B_(b), and M are unknown uponturning on the survey tool. The initial values of these unknowns do nothave to be correct, but the magnitude of the uncertainty is preferablyknown, The initial value of ω_(z0) can be set to be equal to the averageof the first valid outputs from MG_(a) (Ω_(a0)) and MG_(b) (Q_(b0)). Theuncertainty (e.g., standard deviation) of this initial ω_(z0) is notknown, but can without significant loss of accuracy be set to 71% of thebias stability (σ_(B)) given by the microgyro manufacturer. Since B_(a),B_(b), and M have a statistical expectation of zero, this is the initialvalue chosen for these unknowns (B_(a0)=B_(b0)=M₀=0). The uncertaintiesare also unknown, but it is possible to create sufficiently accurateestimations. The bias stability σ_(B) is an obvious candidate for theinitial uncertainties of B_(a0) and B_(b0). These two initial valueswill be correlated with the initial ω_(z0), which can be accounted for.To find the uncertainty in M₀ (σ_(M)) is more complicated, and can bebased on experience. In certain embodiments in which the uncertainty inM₀ is small (e.g., σ_(M) is typically less than 1-2 degrees), usingσ_(M)=1 is sufficient.

The initial state vector and its covariance matrix (which accounts forthe correlation between the initial values) are then given by thefollowing: $\begin{matrix}{{X_{0} = \begin{bmatrix}{\left( {\Omega_{a\quad 0} + \Omega_{b\quad 0}} \right)/2} & 0 & 0 & 0\end{bmatrix}^{T}};\quad{and}} & (11) \\{\Sigma_{s,0} = {\begin{bmatrix}{\sigma_{B}^{2}/2} & {{- \sigma_{B}^{2}}/2.8} & {{- \sigma_{B}^{2}}/2.8} & 0 \\{{- \sigma_{B}^{2}}/2.8} & \sigma_{B}^{2} & 0 & 0 \\{{- \sigma_{B}^{2}}/2.8} & 0 & \sigma_{B}^{2} & 0 \\0 & 0 & 0 & \sigma_{M}^{2}\end{bmatrix}.}} & (12)\end{matrix}$

The predicted state vector at the first update (epoch 1) after timeΔT=(1/frequency) is then X′₁=Φ₁*X₀, where Φ₁ is a matrix extrapolatingthe initial states to epoch 1. In embodiments with a high measurementfrequency, this matrix Φ₁ can be represented by a unit matrix with 4×4dimensions. This matrix Φ₁ will become more complicated if theorientation (e.g., integrated angle), angular accelerations,time-dependent biases, time-dependent misalignments, etc. are modeled.

The covariance matrix of the predicted state vector at epoch 1 is givenby the following:Σ′_(s,1)=Φ₁*Σ_(s,0)*Φ₁ ^(T)+Σ_(Φ,1);  (13)where the transition covariance matrix Σ_(Φ,1) is given by thefollowing: $\begin{matrix}{{\Sigma_{\Phi,1} = \begin{bmatrix}\sigma_{\omega}^{2} & 0 & 0 & 0 \\0 & \sigma_{Bd}^{2} & 0 & 0 \\0 & 0 & \sigma_{Bd}^{2} & 0 \\0 & 0 & 0 & 0\end{bmatrix}};\quad{and}} & (14)\end{matrix}$where σ_(ω)=⅓*(maximum expected angular acceleration)*ΔT andσ_(Bd)=⅓*(maximum expected bias drift rate)*ΔT. This transitioncovariance matrix will become more complicated if the misalignment ismodeled as a time-dependent state (e.g., due to variable bending of thehousing induced by the variable borehole geometry).

At epoch 1, a new set of measurements from MG_(a) and MG_(b) areobtained (Q_(a1) and Q_(b1)). These two measurements can be expressed interms of the states at epoch 1 plus measurement errors (ε_(a) andε_(b)):Ω_(a1)=ω_(z1) +B _(a1)+ε_(a); and  (15)Ω_(b1)=ω_(z1)*cos(M ₁)+B _(b1)+ε_(b).  (16)This is a non-linear equation system, which for simplicity, is madelinear through a Taylor series expansion around the predicted states ofepoch 1:Ω_(a1)=ω′_(z1) +B′ _(a1) +dω _(z1) +dB _(a1)+ε_(a); and  (17)Ω_(b1)=ω′_(z1)*cos(M′ ₁)+B′ _(b1) +dω _(z1)*cos(M′ ₁)−ω′_(z1)*sin(M′₁)*dM ₁ +dB _(b1)ε_(b).  (18)

In matrix form: $\begin{matrix}{{{{A_{1}*{dX}_{1}} + W_{1}} = E};} & (19) \\{{{dX}_{1} = \begin{bmatrix}{d\quad\omega_{z\quad 1}} & {d\quad B_{a\quad 1}} & {d\quad B_{b\quad 1}} & {d\quad M_{1}}\end{bmatrix}^{T}};} & (20) \\{{A_{1} = \begin{bmatrix}1 & 1 & 0 & 0 \\{\cos\left( M_{1}^{\prime} \right)} & 0 & 1 & {{- \omega_{z\quad 1}^{\prime}}*{\sin\left( M_{1}^{\prime} \right)}}\end{bmatrix}};\quad{and}} & (21) \\{{W_{1} = \begin{bmatrix}{\omega_{z\quad 1}^{\prime} + B_{a\quad 1}^{\prime} - \Omega_{a\quad 1}} \\{{\omega_{z\quad 1}^{\prime}*{\cos\left( M_{1}^{\prime} \right)}} + B_{b\quad 1}^{\prime} - \Omega_{b\quad 1}}\end{bmatrix}};} & (22)\end{matrix}$where A₁ is the design matrix, dX₁ is the vector of small corrections tothe predicted states, W is the constant vector at epoch 1, E is theerror vector, and X′₁=[ω′_(z1) B′_(a1) B′_(b1) M′₁]^(T) is the predictedstate vector.

The states Ω_(a1) and Ω_(b1) at epoch 1 are both affected by measurementnoise, as indicated by the error vector. While the amount of noise isunknown, expected measurement standard deviations for one standaloneangular rate measurement (σ_(r)) can be supplied by the manufacturer ofthe microgyro. The value for σ_(r) can be improved through experienceusing subsequent measurements. The measurement covariance matrix for themeasurements at epoch 1 can then be expressed as: $\begin{matrix}{\Sigma_{M,1} = {\begin{bmatrix}\sigma_{r}^{2} & 0 \\0 & \sigma_{r}^{2}\end{bmatrix}.}} & (23)\end{matrix}$

A solution for the small state corrections at epoch 1 can then be foundthrough a least-squares adjustment. This adjustment comprises findingthe dX₁ vector with the minimum matrix product E^(T)*Σ_(M) ⁻¹*E. Themeasured state vector at epoch 1 will then be given by: X₁″=X₁′+dX₁.There are two solutions for the state vector at epoch 1, X1′ and X1″.The optimal estimate for the state vector at epoch 1 will be acovariance-based weighted average of these two solutions. It is possibleto merge the least-squares adjustment and the weighted average into onecalculation step. This merging has the advantage that it will work evenif there are too few measurements present to give a measurement-basedleast-squares solution by itself. The state vector at epoch 1 is throughthe combined method given by:X ₁ =X′ ₁−Σ′_(s,1) *A ₁ ^(T)*(Σ_(M,1) +A ₁*Σ′_(s,1) *A ₁ ^(T))⁻¹*(A ₁*X′ ₁ *W ₁).  (24)The associated covariance matrix, which is a measure for the accuracy ofthe estimated states is given by:Σ_(s,1)=Σ′_(s,1)−Σ′_(s,1) *A ₁ ^(T)*(Σ_(M,1) +A ₁*Σ′_(s,1) *A ₁^(T))⁻¹*(A ₁*Σ′_(s,1)).  (25)The same calculation can be repeated at epoch 2, then for epoch 3, andso on. The matrices, vectors, and equations for epoch k are given by:$\begin{matrix}{{\Phi_{k} = \Phi_{k - 1}};} & (26) \\{{\Sigma_{\Phi,k} = \Sigma_{\Phi,k}};} & (27) \\{{X_{k}^{\prime} = {\Phi_{k}*X_{k - 1}}};} & (28) \\{{\Sigma_{s,k}^{\prime} = {{\Phi_{k}*\Sigma_{s,{k - 1}}*\Phi_{k}^{T}} + \Sigma_{\Phi,k}}};} & (29) \\{{X_{k}^{\prime} = \begin{bmatrix}\omega_{zk}^{\prime} & B_{ak}^{\prime} & B_{bk}^{\prime} & M_{k}^{\prime}\end{bmatrix}^{T}};} & (30) \\{{A_{k} = \begin{bmatrix}1 & 1 & 0 & 0 \\{\cos\left( M_{k}^{\prime} \right)} & 0 & 1 & {{- \omega_{z\quad k}^{\prime}}*{\sin\left( M_{k}^{\prime} \right)}}\end{bmatrix}};} & (31) \\{{W_{k} = \begin{bmatrix}{\omega_{z\quad k}^{\prime}\quad + \quad B_{a\quad k}^{\prime}\quad - \quad\Omega_{a\quad k}} \\{{\omega_{z\quad k}^{\prime}*{\cos\left( M_{k}^{\prime} \right)}}\quad + \quad B_{b\quad k}^{\prime}\quad - \quad\Omega_{b\quad k}}\end{bmatrix}};} & (32) \\{{\Sigma_{M,k} = \Sigma_{M,{k - 1}}};} & (33) \\{{X_{k} = {X_{k}^{\prime} - {\Sigma_{s,k}^{\prime}*A_{k}^{T}*\left( {\Sigma_{M,k} + {A_{k}*\Sigma_{s,k}^{\prime}*A_{k}^{T}}} \right)^{- 1}*\left( {A_{k}*X_{k}^{\prime}*W_{k}} \right)}}};\quad{and}} & (34) \\{\Sigma_{s,k} = {\Sigma_{s,k}^{\prime} - {\Sigma_{s,k}^{\prime}*A_{k}^{T}*\left( {\Sigma_{M,k} + {A_{k}*\Sigma_{s,k}^{\prime}*A_{k}^{T}}} \right)^{- 1}*{\left( {A_{k}*\Sigma_{s,k}^{\prime}} \right).}}}} & (35)\end{matrix}$

Various embodiments of the present invention have been described above.Although this invention has been described with reference to thesespecific embodiments, the descriptions are intended to be illustrativeof the invention and are not intended to be limiting. Variousmodifications and applications may occur to those skilled in the artwithout departing from the true spirit and scope of the invention asdefined in the appended claims.

1. A survey tool for determining an orientation of the survey toolwithin a borehole, the survey tool comprising: a plurality of rotationsensors, each rotation sensor having a sensing axis and a direction ofleast acceleration sensitivity, each rotation sensor adapted to generatea first signal indicative of a detected angular rotation rate about itssensing axis, the plurality of rotation sensors mounted in a housingwith their sensing axes generally parallel to one another and with theirdirections of least acceleration sensitivity generally non-parallel toone another.
 2. The survey tool of claim 1, wherein the plurality ofrotation sensors comprises a plurality of microgyros.
 3. The survey toolof claim 2, wherein the plurality of microgyros comprises at least onevibrating-wheel microgyro.
 4. The survey tool of claim 2, wherein theplurality of microgyros comprises at least one resonating-massmicrogyro.
 5. The survey tool of claim 2, wherein the microgyroscomprise a packed unit with the microgyros stacked on one another. 6.The survey tool of claim 5, wherein the sensing axes of the microgyrosof the packed unit are generally parallel to one another.
 7. The surveytool of claim 2, wherein the microgyros comprise a plurality of packedunits, and wherein the sensing axes of the microgyros of each packedunit are generally colinear to one another and to the sensing axes ofthe microgyros of the other packed units.
 8. The survey tool of claim 7,wherein at least two of the plurality of packed units are spaced apartfrom one another in the housing.
 9. The survey tool of claim 7, whereinthe directions of least acceleration sensitivity of the microgyros ofeach packed unit are spread substantially equally over approximately 180degrees.
 10. The survey tool of claim 1, wherein the sensing axis andthe direction of least acceleration sensitivity of each rotation sensorare generally perpendicular to one another.
 11. The survey tool of claim1, wherein the survey tool is part of a wireline geophysical instrumentpackage.
 12. The survey tool of claim 1, wherein the survey tool is partof a drilling system adapted to drill the borehole.
 13. The survey toolof claim 12, wherein the drilling system comprises a drilling tool, andthe housing of the survey tool is in proximity to the drilling tool. 14.The survey tool of claim 12, wherein the drilling system comprises adrilling tool, and the housing of the survey tool is a component of thedrilling tool.
 15. The survey tool of claim 12, wherein the drillingsystem comprises a measurement-while-drilling (MWD) drilling tool. 16.The survey tool of claim 1, wherein the plurality of rotation sensorscomprises at least three microgyros.
 17. The survey tool of claim 1,wherein the directions of least acceleration sensitivity of theplurality of rotation sensors are spread evenly from one another byapproximately 60 degrees.
 18. The survey tool of claim 1, wherein thedirections of least acceleration sensitivity of the plurality ofrotation sensors are spread evenly from one another by approximately 45degrees.
 19. The survey tool of claim 1, wherein the directions of leastacceleration sensitivity of the plurality of rotation sensors are spreadunevenly over a range of degrees.
 20. The survey tool of claim 1,further comprising a plurality of acceleration sensors mounted in thehousing, each acceleration sensor having a sensing direction, eachacceleration sensor adapted to generate a second signal indicative ofdetected acceleration along its sensing direction.
 21. The survey toolof claim 20, wherein the plurality of acceleration sensors are mountedwith their sensing directions generally parallel to the directions ofleast acceleration sensitivity of the plurality of rotation sensors. 22.The survey tool of claim 20, further comprising a controller thatreceives a first signal from each of the plurality of rotation sensorsand a second signal from each of the plurality of acceleration sensors,the controller calculating a weighted average of the detected angularrotation rates from the plurality of rotation sensors, the weightedaverage including the detected angular rotation rate of each rotationsensor about its sensing axis weighted by the detected accelerationalong its direction of least acceleration sensitivity.
 23. The surveytool of claim 22, wherein the controller is at least partiallypositioned within the housing.
 24. The survey tool of claim 22, whereinthe controller is positioned away from the housing.
 25. The survey toolof claim 22, wherein the controller accesses the first signals and thesecond signals at a discrete frequency.
 26. A control system of arotatably steerable drilling system configured to drill in a selecteddrilling direction of a plurality of drilling directions, the controlsystem configured to adjust the selected drilling direction, the controlsystem comprising: a plurality of rotation sensors, each rotation sensorhaving a sensing axis and a direction of least acceleration sensitivity,each rotation sensor adapted to generate a first signal indicative of adetected angular rotation rate about its sensing axis, the plurality ofrotation sensors mounted in a housing with their sensing axes generallyparallel to one another and with their directions of least accelerationsensitivity generally non-parallel to one another.
 27. A rotatablysteerable drilling system comprising: a drill string configured to drillin a selected direction of a plurality of directions, the drill stringcomprising a drill bit; and a survey tool in proximity to the drill bit,the survey tool comprising: a plurality of rotation sensors, eachrotation sensor having a sensing axis and a direction of leastacceleration sensitivity, each rotation sensor adapted to generate afirst signal indicative of a detected angular rotation rate about itssensing axis, the plurality of rotation sensors mounted in a housingwith their sensing axes generally parallel to one another and with theirdirections of least acceleration sensitivity generally non-parallel toone another.